Freeon theory

In Section 4.4 the freeon ferromagnetic Hamiltonian is used to the develop the freeon theory of spin-waves. 

The freeon theories are converted in to spin theories by means of the Dirac identity, which coverts the freeon Heisenberg to the spin Hamiltonian... 

The mean-field equation will be derived from two models the uniform interaction model and the Ising model. Neither of the two derivations depend explicitly on spin. They will be applied to the freeon theory of ferromagnetism Section 6 and freeon theory of high-Tc superconductivity in Section 7. 

In this section we give the freeon theory of ferromagnetism. As pointed about above ferromagnetism is a second order-phase change which is well-defined by mean-field theory. In Section 6.2 we give the uniform interaction derivation of mean-field theory and in Section 6.3 we compare prediction with observation. 

Note that the undoped cuprate is an antiferromagnet and that doping converts it into a superconductor. We have shown above that antiferromagnetic behavior arises from the z = +1 side of the extended Hiickel-Hubbard spectrum in Fig. 4.1. In the ISB theory the superconducting behavior comes from the z = -1 side of Fig. 4.1 just as does the freeon theory of ferromagnetism. 

The freeon theory of ferromagnetism is based on the negative-U, Hiickel-Hubbard Hamiltonian (NUHH). However the conventional positive-U, Hiickel-Hubbard (PUHH) Hamiltonian employs a positive U which is a measure of the repulsion of a bare pair of electrons on a single site. From whence comes NUHH There are three positions to take with respect to NUHH ... 

In this Section we apply freeon theory to atomic structure. In Section 10.2 we give the freeon Gel fand structures of the second row of the periodic table and in Section 10.3 Gel fand diagrams are used to describe the splitting of d-electron configurations in an octahedral field. 

From all this one must conclude that the determinantal and second-quantized formulations should be regarded as a poor man s group theory which, while convenient, hides the basic freeon dynamics. These fermion methods have the additional disadvantage that their antisymmetric fermion functions are not normally pure spin (freeon) states so that spin-projection may be required. A method for avoiding (approximately) spin projection is the employment of the variation principle to approximate the ground state e. g., unrestricted Hartree-Fock theory. Finally the use of the fermion formulations has lead to the spin paradigm as a replacement for the more fundamental freeon dynamics. 

These facts appear to be unknown to most chemists even after thirty years. During this period I have presented freeon dynamics, on separate occasions, to Nobel-Laureate Robert Mulliken and to my research professor, Henry Eyring, after which I was asked by each whether "they had to learn that stuff ". I was able to assure them that their reputations would not suffer through the neglect of freeon dynamics. Even now after thirty years freeon dynamics does not appear in the standard quantum chemistry texts with the noteworthy exception of Roy McWeeny s Methods of Molecular Quantum Mechanics [2] Consequently the title of this article has been taken to be Freeon Dynamics. A Novel Theory of Atoms and Molecules. When, at the onset of my research on freeon dynamics, I told Norman Hackerman, a former office-mate and at that time president of the University of Texas, that I had an idea for a novel way to do quantum mechanics but that I did not know whether I would be able to acquire the necessary... 

The theory of the application of the unitary group to quantum chemistry (together with relevant references) has been developed in Roy Mcweeny s text [2] and in The Unitary Group in Quantum Chemistry (1986)[5] written in collaboration with Ruben Pauncz. The freeon unitary-group formulation is the... 

The application of second-order perturbation theory to the Hiickel-Hubbard Hamiltonian for z close to one (Section 4.2) yields the freeon, antiferromagnetic, Heisenberg exchange Hamiltonian,... 

The theory employs the spin quantum number which is related to the freeon... 

One of the early great triumphs of atomic theory was the aufbau principle which explained the periodic table. In it the atomic orbital energies were assigned the following order Is < 2s < 2p < 3s <. ..The occupation number of freeon orbitals was limited to no more than two as was discussed in Section 1. Further Hund s rule was imposed i. e. states of highest spin lie the lowest. The Gel fand state reconstruction of the aufbau for the second row of the periodic table (with mi = +1 or zero) is shown in Fig. 10.1 where 2p+ = + 1,2po = 0 and 2p.i = -1 ... 

The flavor and the ordinary orbitals are inert and it is the color orbital which carries the freeon dynamics in the same ways as the freeon (spatial) orbitals carry the dynamics for electronic systems. It should be noted that the two basic field theories are quantum electrodynamics (QED) and quantum chromodynamics (QCD).The color force is also an exchange force in which the several colors are exchanged. 

Electron freeon dynamics, which is also based on group theory, claims the following... 

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